CN111523270A - An improved post-processing method for topology optimization of continuum structures - Google Patents

Abstract

The invention discloses an improved continuum structure topology optimization post-processing method, which is characterized in that: the improved continuum structure topology optimization post-processing method adopts a larger mesh size, that is, the finite element analysis unit size is larger than The default value is 1. When performing topology optimization on the target model, it can effectively avoid the small columnar structure caused by too many meshes. Binarize the optimized model, analyze the optimized model, extract the zigzag boundary line, and obtain the target through numerical calculation. A set of discrete corner points is used as sample points for curve fitting, and the obtained new boundary line is further interpolated to generate a topological structure with a smooth boundary and solidify it. The method proposed by the invention effectively eliminates the sawtooth boundary of the optimized structure, ensures the original design requirements of the optimized structure, reduces the calculation difficulty, reduces the calculation time, enhances the manufacturability of the model, and effectively reduces the difficulty of the post-processing procedure of the topology optimization. .

Description

An improved post-processing method for topology optimization of continuum structures

technical field

The invention relates to the related technical field of structure optimization, in particular to an improved post-processing method for topology optimization of a continuum structure.

Background technique

Topological optimization method is one of the most promising structural optimization methods. This method can effectively utilize materials and make up for the limitation that size and shape optimization cannot change the structural topology. It has received special attention and developed rapidly in recent years due to its flexibility in generating and eliminating small cavities during optimization.

The topology optimization of continuum structure is an important problem of optimization design. At present, the most commonly used topology optimization methods of continuum structure include homogenization method, variable density method, progressive structure optimization method (ESO), level set method (Levelset), independent continuous method. Mapping Method (ICM) etc.

Due to the finite element analysis of the topology optimization structure based on the mesh, the optimization results use the presence or absence of unit bodies to characterize the material characteristics in the continuum structure, resulting in a zigzag shape. If a larger number of elements is used, a finite element model with detailed boundary description and ideal results can be obtained theoretically, and the generation of different optimization results can be avoided. But in fact, due to problems such as network dependence and numerical instability, more elements will generate infinite design variables, making the size of the columnar structure in the optimization result smaller and the number larger, increasing the geometric complexity, and at the same time Increase optimization time. At the same time, the jagged structure boundary makes the results of topology optimization extremely difficult to process, and it is not convenient to import into other CAD software for post-optimization processing. In order to obtain a smooth boundary, further shape optimization is required. If a mapping relationship is used to convert the grid model into a smooth curve or surface model, the processing of the mapping relationship is usually difficult, resulting in time-consuming and labor-intensive realization of the results, which is not ideal.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the shortcomings and deficiencies of the prior art, and to propose an improved post-processing method for topology optimization of continuum structures. When the target model performs topology optimization, it can effectively avoid the small columnar structure caused by the excessive number of meshes; the optimized model is binarized and analyzed, the zigzag boundary line is extracted, and the target discrete corner set is obtained by numerical calculation. It is used as a sample point for curve fitting, which effectively avoids the large deviation between the post-processing model and the original topology optimization model, which affects the structural performance; further interpolation processing is performed on the obtained new boundary line to generate a smooth boundary topology, and the Materialize. This method effectively guarantees the original design requirements of the optimized structure, and avoids grid dependence and checkerboard phenomenon.

In order to achieve the above object, the present invention adopts the following technical solutions, a kind of improved continuum structure topology optimization post-processing method, comprising the following steps:

S1, performing topology optimization processing on the target model to obtain a topology optimization structure.

S2, analyze the obtained topology optimization result to extract a boundary line, and extract the corner points of the zigzag boundary line to obtain a point set P.

S3, perform a smooth connection on the discrete corner points obtained in step S2.

S4 , cutting the obtained closed area of the curve to obtain a smooth closed area of the curve, and then to generate a topology structure with a smooth boundary.

S5, check whether the generated topology structure meets the requirements, and execute step 6, otherwise, reset the parameters and repeat steps S3 to S4.

S6, obtain the final topology structure, and perform substantive processing on it.

Preferably, in the step S1, the topology optimization method of the continuum structure adopts, for example, a variable density method, an incremental structure optimization method (ESO), an independent continuous mapping method (ICM), and the like.

Preferably, in the step S2, the topology optimization result is subjected to binarization processing and mean filtering processing, and the binarization result is converted into a 0-1 numerical matrix. The obtained boundary extraction result is recorded as Z(x, y), and each corner point of the zigzag boundary is identified and calculated. Set the coordinate origin, take the pre-divided discrete unit size as the coordinate unit size, and then determine the coordinates of each corner point to be defined as P _j (x _j , y _j ), forming a point set P={P ₁ , P ₂ , ,P _n }.

Preferably, in the step S3, the length of each straight line segment is determined by the following formula:

为直线段P_iP_i+1的长度，k为距离系数，Δt为预设最小离散单元的大小。in,

is the length of the straight line segment P _i P _i+1 , k is the distance coefficient, and Δt is the size of the preset minimum discrete unit.

The quadratic and cubic spline curves of the least squares method are used to fit the discrete corner point set P obtained in step S3 to form a smooth curve. The degree of smoothness of the smoothed curve is judged, and the criterion is the energy discrimination method. The smaller the energy value, the better the smoothness of the corresponding point set. And observe the curvature map to ensure that the monotonic change of the curvature is as small as possible, the curvature change tends to be as linear as possible, and the change is uniform. The quadratic spline interpolation method is further used for all the obtained lines to form the preliminary results of the closed area of the curve.

Preferably, in the step S6, the data information of the smooth curve boundary line generated by the program is written into a specific TXT file, which is imported into a three-dimensional drawing software and converted into an entity reference for subsequent further operations.

Compared with the prior art, the present invention has the following advantages and beneficial effects:

1. The numerical calculation method used in the present invention is simple, and the calculation time is reduced.

2. The present invention effectively ensures that the characteristics of the topology optimization structure are basically stable, and further ensures that the original design requirements of the optimized structure are within the allowable range.

3. The present invention effectively eliminates the sawtooth boundary of the structure after optimization, makes it a smooth transition, greatly enhances the manufacturability of the model, can be directly used for 3D printing (additive manufacturing technology), numerical control processing, etc., and effectively reduces the post-processing steps of topology optimization. difficulty.

Description of drawings

Fig. 1 is a flow chart of an improved post-processing method for topology optimization of continuum structure of the present invention.

FIG. 2 is a schematic structural diagram of an embodiment of the present invention.

FIG. 3 is a diagram of a topology optimization result according to an embodiment of the present invention.

FIG. 4 is a graph showing the optimization result of binarization processing according to an embodiment of the present invention.

FIG. 5 is a graph showing a result of boundary extraction according to an embodiment of the present invention.

FIG. 6 is an extraction diagram of a corner point of a sawtooth boundary according to an embodiment of the present invention, wherein "*" is the position of the corner point.

FIG. 7 is a topology optimization result of a smooth boundary according to an embodiment of the present invention.

FIG. 8 is a materialized model of an embodiment of the present invention.

Detailed ways

In order to better illustrate the technical solutions of the present invention, the specific embodiments of the present invention are further described in detail below with reference to the accompanying drawings.

The purpose of the present invention is to overcome the shortcomings and deficiencies of the prior art, and to propose an improved continuum structure topology optimization post-processing method, which adopts a smaller number of mesh divisions, that is, the finite element analysis unit size is greater than the default value of 1, When performing topology optimization on the target model, it can effectively avoid the small columnar structure caused by too many meshes; binarize the optimized model, analyze the optimized model, extract the zigzag boundary line, and obtain the target discrete corner set through numerical calculation. , which is used as a sample point for curve fitting, which effectively avoids the large deviation between the post-processing model and the original topology optimization model, which affects the structural performance; further interpolation processing is performed on the obtained new boundary line to generate a smooth boundary topology. , and materialize it. This method effectively guarantees the original design requirements of the optimized structure, and avoids grid dependence and checkerboard phenomenon.

As shown in accompanying drawing 1 is the flow chart of the present invention, as can be seen from the figure, the present invention proposes an improved continuum structure topology optimization post-processing method, comprising the following steps:

In this embodiment, the two-dimensional plane stress structure shown in FIG. 2 is used for description. The design area of the structure is 150mm×40mm, and fixed constraints are adopted for the left and right ends of the design area. The position shown in FIG. 2 is subjected to vertical load. effect. The structure is discretized into 6000 four-node bilinear regular quadrilateral elements, the elastic modulus of the material is taken as E=10 ⁸ , the Poisson's ratio is taken as ν=0.3, and the volume ratio is set as 0.5. Because the structure of the embodiment is a left-right symmetric structure, in order to reduce the amount of calculation, a half structure is used for analysis and calculation during program calculation.

S1, performing topology optimization processing on the target model to obtain a topology optimization structure.

Topological optimization methods for continuum structures are used such as variable density method, progressive structure optimization method (ESO), independent continuous mapping method (ICM) and so on. The patent of the present invention adopts the variable density method, takes the minimum volume weight as the optimization objective, and takes the structural stiffness and displacement as the constraint conditions to perform topology optimization processing on the embodiment, and the optimization result is shown in FIG. 3 .

The optimization problem can be formulated as:

subject to:

是单位杨氏模量的元素刚度矩阵，V(ρ)是材料体积，V₀是设计域的体积，f是预先设定的体积分数，ρ_min是一个包含最低允许相对密度的向量。where C(ρ) is the compliance for a given topology, U is the global displacement vector, F is the global load vector, K is the global stiffness matrix,

is the element stiffness matrix in unit Young's modulus, V(ρ) is the material volume, _V0 is the volume of the design domain, f is the preset volume fraction, and _ρmin is a vector containing the minimum allowable relative density.

S2, analyze the obtained topology optimization result and extract the boundary line, and extract the corner points of the zigzag boundary line to obtain a point set P.

S2-1, performing binarization processing and mean filtering processing on the topology optimization result to obtain an optimization result with clear boundaries, as shown in FIG. 4 . The optimization result is further processed by erosion and expansion and boundary extraction is performed. The graythresh(x) function is called to automatically obtain the threshold value, and the extracted boundary result is binarized again. The result is shown in Figure 5, and the binarized result Convert to a numeric matrix of 0-1.

S2-2, the obtained boundary extraction result is recorded as Z(x, y), and each corner point of the zigzag boundary is identified and calculated.

Calculate the gradients I _x and I _y of Z(x,y) in the x and y directions as follows:

Calculate the product of the gradients of Z(x,y) in the x and y directions as follows:

I_xy＝I_x·I_y

I _xy =I _x ·I _y

The elements X, Y and XY of matrix Q are determined by Gaussian weighting of I _x , I _y and I _xy using a Gaussian function, where σ is taken as 1, as follows:

XY＝(I_xy)

XY=(I _xy )

Calculate the response value R of each node, and set the response value R less than the threshold t to zero. The response value R can be defined as:

R={R:detQ-α(traceQ) ² <t}

Non-maximum suppression is performed on it in the neighborhood, and the point where the local maximum is located is the calculated corner point.

Take the position of the lower left corner of the boundary line in the accompanying drawing 5 as the coordinate origin, take the pre-divided discrete unit size as the coordinate unit size, and then determine that the coordinates of each corner point are defined as P _j (x _j , y _j ), forming a point set P={ P ₁ , P ₂ , ···, P _n }.

S3, perform a smooth connection on the discrete corner points obtained in step S2.

S3-1, the length of each straight line segment is judged by the following formula:

为直线段P_iP_i+1的长度，k为距离系数，Δt为预设最小离散单元的大小。本实施例中取k＝4，Δt＝1。in,

is the length of the straight line segment P _i P _i+1 , k is the distance coefficient, and Δt is the size of the preset minimum discrete unit. In this embodiment, k=4 and Δt=1.

中。The line segments that meet the conditions are stored in the line segment set

middle.

S3-2, for the discrete corner point set P={C(x _m , y _m ), m=1,2,...,n} obtained in step 2, use the quadratic and cubic least squares method for it A spline curve fit forms a smooth curve. Set y=f(x) to minimize the sum of squared errors, namely:

where φ=span{φ ₁ (x),φ ₂ (x),...,φ _m (x)}

p(x)=a ₁ φ ₁ (x)+a ₂ φ ₂ (x)+...+a _m φ _m (x)(m<n)

The degree of smoothness of the smoothed curve is judged, and the criterion is the energy discrimination method. The smaller the energy value, the better the smoothness of the corresponding point set. And observe the curvature map to ensure that the monotonic change of the curvature is as small as possible, the curvature change tends to be as linear as possible, and the change is uniform. The energy value E can be calculated by the following formula:

Among them, e _i is the unit vector in the direction of chord P _i-1 P _i , _ki is the chord length of P _i-1 P _i , |e _i+1 -e _i | represents the chord vector P _i P _i+1 and The amount of change in the direction between P _i-1 P _i , ki ₊₁ + _ki is the sum of the lengths of the two chords.

储存于曲线集

中。The above smoothing spline

save in curve set

middle.

S3-3, cross and merge the obtained line sets L ₁ and L ₂ to obtain a bus set:

And further interpolate the bus set L to form the preliminary result of the closed area of the curve.

S4 , cutting the obtained closed area of the curve to obtain a smooth closed area of the curve, and then to generate a topology structure with a smooth boundary.

S4-1, traverse the line set L={l ₁ ,l ₂ ,...,l _s }, calculate the intersection of any two lines l _i and l _i+1 in the line set L, and denote it as Q _i (x _i , y _i ), and store it in the point set Q={Q ₁ , Q ₂ ,...,Q _n }.

S4-2, take any point Qi from the intersection point set _Q as the starting point, take each line in the line set L as the path, and initially search in a clockwise direction, when the next intersection point Qi ₊₁ is searched, make a judgment, If it is a single path, continue to search along this path; if it is a multi-path, search each path separately, only when the path searched to the next intersection Q _i+2 is a valid path, discard the rest of the invalid paths, and repeat the above operations to continue the search , until the initial point Qi is _searched , and the effective path data of the cyclic search is recorded in the data moment K. When the search for all midpoints and paths is completed, the operation ends, and the final data set K is obtained.

S4-3, the data set K is regenerated into a curve, a smooth closed area of the curve can be obtained, and then a topology structure with a smooth boundary is generated, as shown in FIG. 7 .

S5, check whether the generated topology structure meets the requirements, and execute step 6, otherwise, reset the parameters and repeat steps S3 to S4.

S6, obtain the final topology structure, and perform substantive processing on it.

Write the data information of the smooth boundary curve generated by the program into a specific TXT file, use the curve function to import the TXT data in a 3D software (taking SolidWorks as an example), and generate an entity curve; Corner, rounding, addition, deletion and modification operations, so that 3D printing or CNC machining can be directly carried out. It should be noted that in SolidWorks, the curves generated by this import method cannot be edited directly. You need to create a new sketch and select the Convert Entity Reference function to convert the generated curves into editable entities, as shown in Figure 8.

The descriptions of the above embodiments are only used to further explain the content of the present invention in detail, but do not constitute a limitation on the protection scope of the present invention. On the premise of not departing from the present invention, through logical analysis, reasoning, or modification, equivalent replacement or improvement of the embodiments of the present invention or some of its technical features, all should be deemed to fall within the protection scope of the present invention.

Claims (4)

1. an improved continuum structure topology optimization post-processing method, is characterized in that: comprise the steps: S1, perform topology optimization on the target model to obtain a topology optimization structure, S2, analyze the obtained topology optimization results to extract the boundary line, and extract the corner points of the zigzag boundary line to obtain a point set P, S3, perform a smooth connection on the discrete corner points obtained in step S2, S4, the obtained closed area of the curve is clipped to obtain a smooth closed area of the curve, and then a topology structure with a smooth boundary is generated, S5, check whether the generated topology structure meets the requirements, and perform step 6, otherwise, reset the parameters and repeat steps S3 to S4, S6, obtain the final topology structure, and perform substantive processing on it. 2. a kind of improved continuum structure topology optimization post-processing method according to claim 1, is characterized in that: in described step S2, topology optimization result is carried out binarization processing and mean filter processing, and binary The result is converted into a 0-1 numerical matrix, the obtained boundary extraction result is recorded as Z(x,y), the corner points of the zigzag boundary are identified and calculated, and the coordinate origin is set, and the pre-divided discrete unit size is The size of the coordinate unit is determined, and the coordinates of each corner point are defined as P _j (x _j , y _j ) to form a point set P={P ₁ , P ₂ ,...,P _n }. 3. a kind of improved continuum structure topology optimization post-processing method according to claim 1 is characterized in that: in described step S3, by following formula to judge the length of each straight line segment:

in,

is the length of the straight line segment P _i P _i+1 , k is the distance coefficient, and Δt is the size of the preset minimum discrete unit. 4. a kind of improved continuum structure topology optimization post-processing method according to claim 1 is characterized in that: adopt the quadratic and cubic splines of least squares to the discrete corner point set P obtained in step 2 Fit to form a smooth curve, and judge the degree of smoothness of the smoothed curve. The standard uses the energy discrimination method. The smaller the energy value, the better the smoothness of the corresponding point set. Observe the curvature diagram to ensure the curvature The monotonicity of the change is as small as possible, the curvature change tends to be linear as much as possible, and the change is uniform. The quadratic spline interpolation method is further used for all the obtained lines to form the preliminary results of the closed area of the curve.

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